Partitioning fugacity coefficient from

In the multimedia models used in this series of volumes, an air-water partition coefficient KAW or Henry s law constant (H) is required and is calculated from the ratio of the pure substance vapor pressure and aqueous solubility. This method is widely used for hydrophobic chemicals but is inappropriate for water-miscible chemicals for which no solubility can be measured. Examples are the lower alcohols, acids, amines and ketones. There are reported calculated or pseudo-solubilities that have been derived from QSPR correlations with molecular descriptors for alcohols, aldehydes and amines (by Leahy 1986 Kamlet et al. 1987, 1988 and Nirmalakhandan and Speece 1988a,b). The obvious option is to input the H or KAW directly. If the chemical s activity coefficient y in water is known, then H can be estimated as vwyP[>where vw is the molar volume of water and Pf is the liquid vapor pressure. Since H can be regarded as P[IC[, where Cjs is the solubility, it is apparent that (l/vwy) is a pseudo-solubility. Correlations and measurements of y are available in the physical-chemical literature. For example, if y is 5.0, the pseudo-solubility is 11100 mol/m3 since the molar volume of water vw is 18 x 10-6 m3/mol or 18 cm3/mol. Chemicals with y less than about 20 are usually miscible in water. If the liquid vapor pressure in this case is 1000 Pa, H will be 1000/11100 or 0.090 Pa m3/mol and KAW will be H/RT or 3.6 x 10 5 at 25°C. Alternatively, if H or KAW is known, C[ can be calculated. It is possible to apply existing models to hydrophilic chemicals if this pseudo-solubility is calculated from the activity coefficient or from a known H (i.e., Cjs, P[/H or P[ or KAW RT). This approach is used here. In the fugacity model illustrations all pseudo-solubilities are so designated and should not be regarded as real, experimentally accessible quantities. 

Equation A1.3 shows that isotope effects calculated from standard state free energy differences, and this includes theoretical calculations of isotope effects from the partition functions, are not directly proportional to the measured (or predicted) isotope effects on the logarithm of the isotopic pressure ratios. Rather they must be corrected by the isotopic ratio of activity coefficients. At elevated pressures the correction term can be significant, and in the critical region it may even predominate. Similar considerations apply in the condensed phase except the fugacity ratios which define Kf are replaced by activity ratios, a = Y X and a = y C , for the mole fraction or molar concentration scales respectively. In either case corrections for nonideality, II (Yi)Vi, arising from isotope effects on the activity coefficients can be considerable. Further details are found in standard thermodynamic texts and in Chapter 5. 

Figure 10.13 Effect of oxygen fugacity on conventional partition coefficient of Cr. (A) Olivine/liquid partitioning experimental data of Bird (1971), Weill and McKay (1975), Huebner et al. (1976), Lindstrom (1976), and McKay and Weill (1976). (B) Subcalcic py-roxene/liquid partitioning experimental data of Schreiber (1976). Reprinted from A.J. Irving, Geochimica et Cosmochimica Acta, 42, 743-770, copyright 1978, with kind permission from Elsevier Science Ltd., The Boulevard, Langford Lane, Kidlington 0X5 1GB, UK.

It is also apparent (Fig. 6.29) that Kp correlates with the octanol-air partition coefficient, Moa. and this would follow from the fact that pl can be expressed as a linear function of Kq - In the equilibrium distribution of a compound between the vapor phase and octanol, the fugacity or partial pressure of the compound in... 

TABLE 1 gives the reported values or ranges of the physical-chemical properties of chlorobenzenes (CBs), polychlorinated biphenyls (PCBs) and polychlorinated dibenzo-p-dioxins (PCDDs). Fugacity ratios were obtained from a single estimated entropy of fusion of 56 J mol °K (Yalkowsky 1979), molar volumes were calculated by the Le Bas method, an additive group contribution method (Reid et al. 1977). Total surface area (TSA) values were obtained from Yalkowsky et al. (1979 a,b). Solubilities, vapour pressures and octanol/water partition coefficients (Andren et al. 1986 Shiu and Mackay 1986 Bobra et al. 1985) are also tabulated. Henry s law constants were calculated as PSl/C and the octanol solubility Q as C Kq, . 

The fugacity capacity for other phases can be calculated from the chemical s partition coefficient between that phase and water and the chemical s Henry s law constant. For water, the fugacity capacity is... 

Therefore, the key information required to quantify chemical mobility are the numerical values of the MTCs, concentrations in the phases and the equilibrium partition coefficient, or correspondingly the respective fugacities. The direction of the diffusive flux can be inferred from the fiigacity gradient or difference diffusion is directed from high to low fiigacity. 

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